Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#import<cstdio>

template<typename ...> static inline int gc(void) { return getchar(); }
static inline void read(int &x){int k,m(0);x=0;for(;;){k=gc();if(48<=k&&k<=57){x=k-48;break;}}for(;;){k=gc();if(k<48||k>57)break;x=(x<<3)+(x<<1)+k-48;}}

int N, d[262144], p, x, i;

int main(){
    read(N);
    i = N;
    for(; i; d[x] = --i)read(x);
    i = N;
    for(; --i;)p ? d[N] > d[i] ^ d[i] > d[i + 1] ^ d[i + 1] > d[N] ? ++p, N = i + 1 : 0 : d[i] > d[i + 1] ? --N : ++p;
    printf("%d", p);
}